Question

sqrt(18 + 12sqrt(2)) giúp e vs ạ

Answer 1

\(\sqrt{18+12\sqrt{2}}\)

\(=\sqrt{6\cdot\left(3+2\sqrt{2}\right)}\)

\(=\sqrt{6\cdot\left[\left(\sqrt{2}\right)^2+2\cdot\sqrt{2}\cdot1+1^2\right]}\)

\(=\sqrt{6\left(\sqrt{2}+1\right)^2}\)

\(=\sqrt{6}\cdot\left|\sqrt{2}+1\right|\)

\(=\sqrt{6}\cdot\left(\sqrt{2}+1\right)\)

\(=\sqrt{12}+\sqrt{6}\)

\(=2\sqrt{3}+\sqrt{6}\)

Answer 2

\(\sqrt{18+12\sqrt{2}}\)

\(=\sqrt{6\left(3+2\sqrt{2}\right)}=\sqrt{\left(\sqrt{6}\cdot\sqrt{2}+\sqrt{6}\right)^2}\)

\(=\left|\sqrt{12}+\sqrt{6}\right|=2\sqrt{3}+\sqrt{6}\)